Probability and sports

### Abstract

This lesson is devoted to Internet research on a specific topic: finding topics in sports where probability is relevant. The goal of the lesson is to introduce some statistics and probability concepts by looking at practical questions that arise in professional sports.

### Objectives

Upon completion of this lesson, students will:

• have seen that knowledge of probability concepts is useful when looking at sports
• have learned to search for a specific topic on the internet

### Standards

The activities and discussions in this lesson address the following NCTM standards:

Data Analysis and Probability

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

• formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population
Develop and evaluate inferences and predictions that are based on data
• use observations about differences between two or more samples to make conjectures about the populations from which the samples were taken
Understand and apply basic concepts of probability
• understand and use appropriate terminology to describe complementary and mutually exclusive events
• use proportionality and a basic understanding of probability to make and test conjectures about the results of experiments and simulations
• compute probabilities for simple compound events, using such methods as organized lists, tree diagrams, and area models

### Student Prerequisites

• Arithmetic: Students must be able to:
• relate the sports information they collect to mathematical expression
• use simple addition, subtraction, multiplication and division when working with the sports information they collect
• Technological: Students must be able to:
• perform basic mouse manipulations such as point, click and drag
• use a browser such as Netscape for experimenting with the activities

### Teacher Preparation

Students will need:

• Pencil and Paper

### Key Terms

This lesson introduces students to the following terms through the included discussions:

### Lesson Outline

1. Focus and Review

Remind students of what they learned in previous lessons that will be pertinent to this lesson and/or have them begin to think about the words and ideas of this lesson:

• How many of you like to play sports?
• When you are getting ready to play a game, are there some teams that you know your team can beat easier than others?

2. Objectives

Let the students know what they will be doing and learning today. Say something like this:

• Today, class, we are going to learn how probability applies to sports.
• We are going to use the computers to learn about applying probability to sports, but please do not turn your computers on until I ask you to. I want to show you a little about this activity first.

3. Teacher Input
• review some basic probability facts and explain to the students what they will be doing.

4. Guided Practice

• Have each person or group decide which sport they would like to research and monitor them as they begin their searches.
• You can suggest people search for probability information in the web sites related to the following sports:

5. Independent Practice

• Have students search one of the four sports provided (or find information about a different sport, if desired) to find connections between the sport and probability. Each student or group of students can find and then share a piece of information about chances to win against a particular player or team, chances to make a "hole in one" in golf, chances of making a basket in basketball, or anything else connected with probability that they may find on these sports pages.

• Search for answers to specific questions. Each student or group of students can come up with specific questions concerning sports, and try to find answers using Internet resources. These sample questions about golf can be used as examples.

• Sports challenge: "Do you believe it?" Students or groups of students find piece of probability information on sports, and then challenge another group to confirm or refute their data. Students do not necessarily give the correct answer, making the activity more interesting. For example, having found that the record drive for a long drive in a golf contest is 448 yards, the students may challenge another group: "Is it true that the record drive is above 470 yards?" Students can give hints, for example, the address of the website where they have found the information.
6. Closure

• You may wish to bring the class back together for a discussion of the findings. Once the students have been allowed to share what they found, summarize the results of the lesson.

### Alternate Outlines

This lesson can be rearranged in several ways.

### Suggested Follow-Up

After this lesson, the students will have seen practical applications of how probability is used in everyday situations such as sports. The next lesson, Ideas That Lead to Probability, introduces ideas that are the basis of probability theory. By using everyday experiences and intuitive understanding, this lesson gives students a gradual introduction to probability. Students will work with random number generators learn what it means for a game to be fair.